Synapse

Synapse is the "New Continent" that Sugata has been searching for and found out that it's connected to Tomoki's dream. The only way for them to enter Synapse though, is through the Dive Game. Sugata finds that some people on earth are not "real", but in fact are just angels inside pods "dreaming" and that it is where the Angeloids had been developed.

Background
Synapse first appears as a grassy field through Tomoki's dreams. However, later when Sugata keeps re-entering, it's revealed that Synapse is divided into separate "islands", some islands are organic while others are not. The land has been here for Eons. The exact size of Synapse in unknown. What is shown is that the dimension houses a star. Nymph in Pandora Form, who was at least light speed, took minutes traveling though Synapse to make her way to Zeus. Which means Synapse is massively bigger than Earth. The angels that live there created the Big Bang. According to Hiyori in the My Eternal Master movie, Synapse created and rule over multiple timelines of parallel universes and universes of different time axis in the Hyper-Dimension.

Tomoki, Sohara, Sugata, and Mikako visited an island with a single large structure with mysterious writings on it. Chapter 72 of the manga reveals that the scrawling marks are the wishes of every Angel from Synapse, all wishing for a new world. This structure (named "The Rule") can grant any wish to any non-Angeloid who uses it.

Aside from Tomoki's dream, the only other way to reach Synapse is to fly there through the entry portal. However, any intruders in Synapse airspace will come under attack by a specialized, anti-air defense system, "Zeus."

The mass-produced Medical Specialist Angeloids clean and maintain Synapse. These Angeloids are closer to what humans call robots than to an Angeloid (according to Nymph). These Angeloids are made for maintaining the city for when the people of Synapse are dreaming.

Inhabitants
inhabitants of Synapse started out just like humans did on Earth, by evolving and either died or grew wings. The inhabitants of Synapse have lived for eons. They developed many high-tech machinery and other scientific inventions that appear to be magical to modern humans. After living for eons, Daedalus and the rest the inhabitants began to get bored and unhappy. Daedalus, in an attempt to solve this problem, created the Rule, which had the ability to grant all the inhabitants wishes. After having all their wishes granted, the inhabitants of Synapse were happy for a while, but soon after all their wishes and dreams had come true, they began to face a collective existential crisis. Eventually, the inhabitants began to die by suicide. Over time, the population of synapse decreased from millions to only three thousand. In an attempt to solve this problem, Daedalus and the rest of Synapse tried to create a new world/universe with the Rule, so they recreated the universe. How they did this is not explained in the anime. (In the last chapters of the manga, it is explained how they recreated the universe. Firstly, Synapse ceases to exist, and after everything, be it the people, animals, plants, and even the sky will be destroyed.)

This didn't change anything, so they created the human species and Daedalus presumably created the first generation of angeloids alongside Minos. Daedalus and the rest of Synapse created the humans and the Angeloid for their amusement, if only for an hour. They began to watch the humans, and after a while of watching them, Daedalus and the rest of the inhabitants of Synapse began to become jealous of the humans. The humans had what they coveted so much: the ability to dream. To acquire what they wished for the most, Daedalus along with the rest of Synapse, created a dome with machines to put themselves in a dream-like state. After they completed their objective, Daedalus along with most of Synapse's inhabitant went into the dome to be put into a new dream life where they lived among the humans on Earth by projecting their consciousness into artificial humans.